6)= -1...

krysolov1 @krysolov1

August 2022 1 12 Report

помогите с решением 2sin(3x-pi/6)= -1

Answers & Comments

mukus13

Verified answer

$2sin(3x- \frac{ \pi }{6})=-1$

$sin(3x- \frac{ \pi }{6})=- \frac{1}{2}$

$3x- \frac{ \pi }{6}=(- 1)^{k} arcsin(- \frac{1}{2})+ \pi k,$ $k$ ∈ $Z$

$3x- \frac{ \pi }{6}=(- 1)^{k}(- \frac{ \pi }{6} )+ \pi k,$ $k$ ∈ $Z$

$3x- \frac{ \pi }{6}=(- 1)^{k+1}\frac{ \pi }{6} + \pi k,$ $k$ ∈ $Z$

$3x=(- 1)^{k+1}\frac{ \pi }{6}+ \frac{ \pi }{6} + \pi k,$ $k$ ∈ $Z$

$x=(- 1)^{k+1}\frac{ \pi }{18}+ \frac{ \pi }{18} + \frac{\pi k}{3} ,$ $k$ ∈ $Z$

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